### CFA Practice Question

A company has issued 20-year bonds paying 5.5% coupon, semiannually, at a price of 98.8% of face value. The dividend yield on its stock is estimated at 4.5%. The stock price appreciation rate is 6%. What is the company's cost of capital if it is in the 34% marginal tax bracket and its debt-to-equity ratio is 50%?
A. 14.20%
B. 7.10%
C. 8.23%
Explanation: We first compute the cost of debt based on the bond issue: PV = -98.8; FV = 100; PMT = 2.75; N = 40; CPT I/Y = 2.80 s.a., or 5.60% annually.

Next, we compute the weights. Since D/E = 0.5, for every dollar of equity there is 0.50 in debt. Thus, debt is 1/3rd and equity is 2/3rd of total capital.

Cost of equity is estimated by adding the dividend and capital gains yield = 4.5% + 6% = 10.5%.

We finally apply the weighted average cost of capital formula: WACC = 5.6 x (1 - 0.34) x (1/3) + 10.5 x (2/3) = 8.23%.

User Comment
rickeling I don't follow line 2 of the answer. How do we get from a debt:equity of 0.5 to "Thus 1/3rd debt...". Surely 0.5 = 50% debt, 50% equity?

What have I missed?
patsy Maths. Use an example: if debt is 100 then equity is 200 (to observe the 50% ratio). So total capital is 300 and the weights are 1/3 debt and 2/3 equity.
mc01 couldnt explain it better than pasty.
cahiz84 Use to D/C formula

D/C = (D/E)/1+(D/E)

0.5/1.5=0.33 ---- 1/3 is debt and 2/3 is equity
Widokas 2.8 x 2 = 5.6 semmianual ield is not the same as effective yield (which we use in capital cost estimation) 1.028 ^ 2 - 1 = 5.68. is it a mistake in the answer?
charliedba No Widokas. From semi to annual you should always double for simplicity.
jpducros Cost of equity = dividend yield + capital gain yield.
It make full sense.
kutch rickeling

debt-to-equity = total debt/total equity = 0.5

meaning the numerator is only half of the denominator
kutch hence the total is the numerator(eg. 1) plus the denominator(1+1 = 2) which is equal to 3
czar great question!
Sam123456 I think it's easier just to say debt/equity = 1/2 = 0.5
jdcfa987 I dont understand how we are able to use the div yield + capital gain yield...can someone explain?
degosan9 Cost of common stock is D1/P0 + g

D1: upcoming dividend
P0: current price
D1/P0= dividend yield(given as 4.5%)
g=growth rate(appreciation rate, given as 6%)

4.5+6=10.5
chesschh took me some time to understand it completely, but worth it.